Abstract

The condition that limits the volume that will sustain fundamental mode operation in a YAG:Nd laser has been determined. The relationship between the pump lamp power and fundamental mode power has been derived which correctly predicts the single mode power. The analysis incorporates the results of a computer analysis of the laser rod, which, among other things, computes the heat absorbed per unit volume and plots the isotherms for the interior of the rod. Recommendations for the design of high power, fundamental mode lasers are given.

© 1970 Optical Society of America

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References

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  1. H. Kogelnik, Bell Syst. Tech. J., 44, 455 (1965).
  2. A. Ashkin, G. O. Boyd, J. M. Dziedzic, Phys. Rev. Lett. 11, 14 (1963).
    [CrossRef]
  3. L. M. Osternik, J. D. Foster, Appl. Phys. Lett. 12, 168 (1968).
    [CrossRef]
  4. N. F. Borelli, M. L. Charters, J. Appl. Phys. 36, 2172 (1965).
    [CrossRef]
  5. F. W. Quelle, Appl. Opt. 5, 633 (1966).
    [CrossRef] [PubMed]
  6. S. D. Sims, A. Stein, C. Roth, Appl. Opt. 6, 579 (1967).
    [CrossRef] [PubMed]
  7. S. Epstein, J. Appl. Phys. 38, 2715 (1967).
    [CrossRef]
  8. E. P. Reidel, G. D. Baldwin, J. Appl. Phys. 38, 2720 (1967).
    [CrossRef]
  9. G. D. Baldwin, E. P. Riedel, J. Appl. Phys. 38, 2726 (1967).
    [CrossRef]
  10. E. Condon, H. Odishaw, in Handbook of Physics (McGraw-Hill, New York, 1967), pp. 5–61.
  11. S. B. Shuldt, R. L. Aagard, Appl. Opt. 3, 509 (1963).
    [CrossRef]
  12. W. C. Fricke, Final report for IR&D program NRB (1968–1969) conducted at Sanders Associates, Nashua, N.H.
  13. A. Yariv, J. P. Gordon, Proc. IEEE, 51, 4 (1963).
    [CrossRef]
  14. S. E. Miller, Bell Syst. Tech. J. 44, 201(1965).
  15. P. H. Klein, W. J. Croft, J. Appl. Phys. 38, 1603 (1967).
    [CrossRef]
  16. J. D. Foster, L. M. Osterink, Appl. Opt. 7, 2428 (1968).
    [CrossRef] [PubMed]
  17. H. S. Yoder, M. L. Keith, Amer. Mineral 36, 519 (1951).
  18. W. Smith, P. Sorokin, The Laser (McGraw-Hill, New York, 1966), p. 75.
  19. Z. J. Kiss, R. J. Pressley, Proc IEEE 54, 1236 (1966).
    [CrossRef]

1968 (2)

L. M. Osternik, J. D. Foster, Appl. Phys. Lett. 12, 168 (1968).
[CrossRef]

J. D. Foster, L. M. Osterink, Appl. Opt. 7, 2428 (1968).
[CrossRef] [PubMed]

1967 (5)

P. H. Klein, W. J. Croft, J. Appl. Phys. 38, 1603 (1967).
[CrossRef]

S. D. Sims, A. Stein, C. Roth, Appl. Opt. 6, 579 (1967).
[CrossRef] [PubMed]

S. Epstein, J. Appl. Phys. 38, 2715 (1967).
[CrossRef]

E. P. Reidel, G. D. Baldwin, J. Appl. Phys. 38, 2720 (1967).
[CrossRef]

G. D. Baldwin, E. P. Riedel, J. Appl. Phys. 38, 2726 (1967).
[CrossRef]

1966 (2)

Z. J. Kiss, R. J. Pressley, Proc IEEE 54, 1236 (1966).
[CrossRef]

F. W. Quelle, Appl. Opt. 5, 633 (1966).
[CrossRef] [PubMed]

1965 (3)

S. E. Miller, Bell Syst. Tech. J. 44, 201(1965).

N. F. Borelli, M. L. Charters, J. Appl. Phys. 36, 2172 (1965).
[CrossRef]

H. Kogelnik, Bell Syst. Tech. J., 44, 455 (1965).

1963 (3)

A. Ashkin, G. O. Boyd, J. M. Dziedzic, Phys. Rev. Lett. 11, 14 (1963).
[CrossRef]

S. B. Shuldt, R. L. Aagard, Appl. Opt. 3, 509 (1963).
[CrossRef]

A. Yariv, J. P. Gordon, Proc. IEEE, 51, 4 (1963).
[CrossRef]

1951 (1)

H. S. Yoder, M. L. Keith, Amer. Mineral 36, 519 (1951).

Aagard, R. L.

S. B. Shuldt, R. L. Aagard, Appl. Opt. 3, 509 (1963).
[CrossRef]

Ashkin, A.

A. Ashkin, G. O. Boyd, J. M. Dziedzic, Phys. Rev. Lett. 11, 14 (1963).
[CrossRef]

Baldwin, G. D.

E. P. Reidel, G. D. Baldwin, J. Appl. Phys. 38, 2720 (1967).
[CrossRef]

G. D. Baldwin, E. P. Riedel, J. Appl. Phys. 38, 2726 (1967).
[CrossRef]

Borelli, N. F.

N. F. Borelli, M. L. Charters, J. Appl. Phys. 36, 2172 (1965).
[CrossRef]

Boyd, G. O.

A. Ashkin, G. O. Boyd, J. M. Dziedzic, Phys. Rev. Lett. 11, 14 (1963).
[CrossRef]

Charters, M. L.

N. F. Borelli, M. L. Charters, J. Appl. Phys. 36, 2172 (1965).
[CrossRef]

Condon, E.

E. Condon, H. Odishaw, in Handbook of Physics (McGraw-Hill, New York, 1967), pp. 5–61.

Croft, W. J.

P. H. Klein, W. J. Croft, J. Appl. Phys. 38, 1603 (1967).
[CrossRef]

Dziedzic, J. M.

A. Ashkin, G. O. Boyd, J. M. Dziedzic, Phys. Rev. Lett. 11, 14 (1963).
[CrossRef]

Epstein, S.

S. Epstein, J. Appl. Phys. 38, 2715 (1967).
[CrossRef]

Foster, J. D.

L. M. Osternik, J. D. Foster, Appl. Phys. Lett. 12, 168 (1968).
[CrossRef]

J. D. Foster, L. M. Osterink, Appl. Opt. 7, 2428 (1968).
[CrossRef] [PubMed]

Fricke, W. C.

W. C. Fricke, Final report for IR&D program NRB (1968–1969) conducted at Sanders Associates, Nashua, N.H.

Gordon, J. P.

A. Yariv, J. P. Gordon, Proc. IEEE, 51, 4 (1963).
[CrossRef]

Keith, M. L.

H. S. Yoder, M. L. Keith, Amer. Mineral 36, 519 (1951).

Kiss, Z. J.

Z. J. Kiss, R. J. Pressley, Proc IEEE 54, 1236 (1966).
[CrossRef]

Klein, P. H.

P. H. Klein, W. J. Croft, J. Appl. Phys. 38, 1603 (1967).
[CrossRef]

Kogelnik, H.

H. Kogelnik, Bell Syst. Tech. J., 44, 455 (1965).

Miller, S. E.

S. E. Miller, Bell Syst. Tech. J. 44, 201(1965).

Odishaw, H.

E. Condon, H. Odishaw, in Handbook of Physics (McGraw-Hill, New York, 1967), pp. 5–61.

Osterink, L. M.

Osternik, L. M.

L. M. Osternik, J. D. Foster, Appl. Phys. Lett. 12, 168 (1968).
[CrossRef]

Pressley, R. J.

Z. J. Kiss, R. J. Pressley, Proc IEEE 54, 1236 (1966).
[CrossRef]

Quelle, F. W.

Reidel, E. P.

E. P. Reidel, G. D. Baldwin, J. Appl. Phys. 38, 2720 (1967).
[CrossRef]

Riedel, E. P.

G. D. Baldwin, E. P. Riedel, J. Appl. Phys. 38, 2726 (1967).
[CrossRef]

Roth, C.

Shuldt, S. B.

S. B. Shuldt, R. L. Aagard, Appl. Opt. 3, 509 (1963).
[CrossRef]

Sims, S. D.

Smith, W.

W. Smith, P. Sorokin, The Laser (McGraw-Hill, New York, 1966), p. 75.

Sorokin, P.

W. Smith, P. Sorokin, The Laser (McGraw-Hill, New York, 1966), p. 75.

Stein, A.

Yariv, A.

A. Yariv, J. P. Gordon, Proc. IEEE, 51, 4 (1963).
[CrossRef]

Yoder, H. S.

H. S. Yoder, M. L. Keith, Amer. Mineral 36, 519 (1951).

Amer. Mineral (1)

H. S. Yoder, M. L. Keith, Amer. Mineral 36, 519 (1951).

Appl. Opt. (4)

Appl. Phys. Lett. (1)

L. M. Osternik, J. D. Foster, Appl. Phys. Lett. 12, 168 (1968).
[CrossRef]

Bell Syst. Tech. J. (2)

H. Kogelnik, Bell Syst. Tech. J., 44, 455 (1965).

S. E. Miller, Bell Syst. Tech. J. 44, 201(1965).

J. Appl. Phys. (5)

P. H. Klein, W. J. Croft, J. Appl. Phys. 38, 1603 (1967).
[CrossRef]

N. F. Borelli, M. L. Charters, J. Appl. Phys. 36, 2172 (1965).
[CrossRef]

S. Epstein, J. Appl. Phys. 38, 2715 (1967).
[CrossRef]

E. P. Reidel, G. D. Baldwin, J. Appl. Phys. 38, 2720 (1967).
[CrossRef]

G. D. Baldwin, E. P. Riedel, J. Appl. Phys. 38, 2726 (1967).
[CrossRef]

Phys. Rev. Lett. (1)

A. Ashkin, G. O. Boyd, J. M. Dziedzic, Phys. Rev. Lett. 11, 14 (1963).
[CrossRef]

Proc IEEE (1)

Z. J. Kiss, R. J. Pressley, Proc IEEE 54, 1236 (1966).
[CrossRef]

Proc. IEEE (1)

A. Yariv, J. P. Gordon, Proc. IEEE, 51, 4 (1963).
[CrossRef]

Other (3)

W. Smith, P. Sorokin, The Laser (McGraw-Hill, New York, 1966), p. 75.

W. C. Fricke, Final report for IR&D program NRB (1968–1969) conducted at Sanders Associates, Nashua, N.H.

E. Condon, H. Odishaw, in Handbook of Physics (McGraw-Hill, New York, 1967), pp. 5–61.

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Figures (11)

Fig. 1
Fig. 1

The power absorbed in the volume δV is computed by assuming the pump lamp power diffused by the lambertian scatterer dA and that the intensity of pump radiation along ρ decreases exponentially due to absorption.

Fig. 2
Fig. 2

Definition of the ellipse parameters for the pump cavity.

Fig. 3
Fig. 3

Intensity on rod surface vs angle.

Fig. 4
Fig. 4

Power absorbed per unit volume for a 0.634 cm × 7.5 cm, 1.2 at% Nd:YAG laser rod vs radius along three diameters.

Fig. 5
Fig. 5

Power absorbed per cm3 for a 0.634 cm × 7.5 cm, 1.2 at% Nd:YAG laser rod vs angle for six values of radius.

Fig. 6
Fig. 6

Isothermal lines inside a laser rod.

Fig. 7
Fig. 7

Experimental setup for measuring the leasing effects of the YAG:Nd laser rod in a single elliptical pump cavity.

Fig. 8
Fig. 8

Pump lamp power vs divergence of the He–Ne beam after passing through the YAG:Nd laser rod pumped in a single elliptical cavity.

Fig. 9
Fig. 9

Fundamental mode output as pump power for a 0.634-cm/7.5-cm YAG:Nd laser rod pumped in a single elliptical cavity.

Fig. 10
Fig. 10

Area inside ΔT (°C) determined from the computer generated isotherms for a 0.634 = cm × 7.5 = cm YAG:Nd laser rod pumped in a single elliptical cavity at 2000 W, 2400 W, 2700 W, and 3000 W.

Fig. 11
Fig. 11

The ratio of the areas which have the same ΔT for two pumping rates as determined from Fig. 10. The experimentally determined ratios from Table I and indicated on each curve along with the corresponding temperature variations ΔT (°C).

Tables (1)

Tables Icon

Table I The Maximum Temperature Variation Determined by the Experimentally Determined Ratio of the Areas at Two Pump Powers

Equations (36)

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2 T + U / k = 0.
U ( r , φ , z ) = φ s z s ( 1 R ) α P s ( φ s , z s ) cos ( θ ) e ρ / λ π ρ 2 λ ,
ρ 2 = r o 2 + r 2 2 r r o cos ( φ s φ ) + ( z z s ) 2 ,
cos θ = [ r o r cos ( φ s φ ) ] / ρ ,
θ e ( rad ) = ( 5.61 ± 0.64 ) × 10 7 P + ( 2.67 ± 0.15 ) × 10 3 .
θ e ( rad ) = 1.1 × 10 4 U + ( 2.59 ± 0.06 ) × 10 3
U = α P ,
α = ( 5.1 ± 0.6 ) × 10 3 cm 3 .
U 1.06 3 4 α P ( W ) ,
U 1.06 3.8 × 10 3 P ( W ) .
U 1.06 th = 3.8 × 10 3 P th ( W cm 3 )
P f c V = 4 π 2 h ν 3 Δ ν L 3 t photon = ( 3.8 ± 1.0 ) W cm 3
P 1.06 = ( U 1.06 U 1.06 thresh ) V ,
P 1.06 = ( 3 4 α L A ) ( P P th ) .
W 00 < P 1.06 .
W 00 = P f c ( P R 1 ) = ( 4 π 2 h ν 3 Δ ν c 3 t phot ) ( V ) ( P R 1 ) = a A ( P P th ) ,
W 1 = a A 1 ( P 1 P th ) , W 2 = a A 2 ( P 2 P th ) .
A 1 / A 2 = ( W 1 / W 2 ) [ ( P 2 P th ) / ( P 1 P th ) ] .
Δ L = ( L opt T ) Δ T = α T L ( n + n α T T ) Δ T = 0.0915 μ
r o 2 = 4 k Δ T U = 4 k Δ L / [ L α T U ( n + n α T T ) ] .
A = 4 π k Δ L / [ L α T α P ( n + n α T T ) ] = 1111 + 175 L ( cm ) P ( W )
a = a ( L / P th ) ,
P 1.06 W 00
a 3 4 α L ,
a 3 4 α P th ( 6 ± 2 ) ( W cm 3 ) .
a P f c / V ( 3.8 ± 1.0 ) ( W cm 3 ) .
a = ( 2.5 ± 0.1 ) ( W cm 3 ) .
W 00 = { 4 π k a Δ L / [ α T α ( n + n α T T ) ] } ( 1 P th 1 P ) ,
W 00 = ( 3530 ± 550 ) ( 1 / 1570 1 / P ) ( W )
W 00 = ( 4090 ± 125 ) ( 1 1570 1 P ) ( W )
P th α ( 1 / L E ) .
A = 4 π k Δ L / [ L α T α P ( n + n α T T ) ] .
W 00 = { 4 π k a Δ L / [ α T α ( n + n α T T ) ] } ( 1 P th 1 P ) .
W 00 = ( 3530 ± 550 ) ( 1 / 1570 1 / P ) W ,
W 00 = ( 4090 ± 125 ) ( 1 / 1570 1 / P ) W ,
W 00 = a A ( P P th )

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